840,?, 420, 140, 35, 7

Series pattern
x 2 + 5, x 3 + 5, x 4 + 5, x 5 + 5,
? Missing term = 104 x 4 + 5 = 416 + 5 = 421

Series pattern
1³ + 1, 3³ + 1, 4³ + 1, 5³ + 1
? Missing term = 6³ + 1 = 217

Series pattern
2 x 1², 2 x 2², 2 x 3², 2 x 4², 2 x 5², 2 x 6²
? Missing term = 2 x 4² = 32

T₅ = a + 4d, T₇ = a + 6d
? 5(a + 4d) = 7(a + 6d)
? 5a + 20d = 7a + 42d
? a = -11d
? T₁₂ = a + 11d = - 11d + 11d = 0
So, the twelfth term is 0.

The second and fourth term of the HP are 1/6 and 1/14 respectively,
Hence, for the corresponding AP, the second term is 6 and fourth term is 14.
Hence a + d = 6 and a + 3d = 14
? 2d = 8
? d = 4 and a = 2

Hence, the 10th term of this AP = a + (10 -1)d
= 2 + (10 - 1)x 4 = 2 + 9 x 4
= 2 + 36 = 38
Hence, for the corresponding HP, the 10th term is 1/38.

Series pattern - 45, - 35, -25,...
? Missing term = 45 - 25 = 20

Series pattern +15, + 30, +60, +120
? Missing term = 49 + 60 = 109

Series pattern = (2 x Previous number) + 2
? Missing term = 2 x 30 +2 = 62

Series pattern
7 + 9 = 16,
9 + 16 = 25,
16 + 25 = 41,
25 + 41 = 66
Should come in place of 68
41 + 66 = 107,
66 + 107 = 173
Clearly, 68 is wrong and will be replaced by 66.

Series pattern
16 x 0.25 = 4,
4 x 0.50 = 2,
2 x 0.75 =1.5,
1.5 x 1.00 = 1.5
Should come in place of 1.75
1.5 x 1.25 = 1.875
Clearly, 1.75 is wrong and will be replaced by 1.5